Abstract

We report the first Bragg gratings fabricated by Focused Ion Beam milling in optical waveguides. We observe striking features in the optical transmission spectra of surface relief gratings in silicon-on-insulator waveguides and achieve good agreement with theoretical results obtained using a novel adaptation of the beam propagation method and coupled mode theory. We demonstrate that leaky Higher Order Modes (HOM), often present in large numbers (although normally not observed) even in nominally single mode rib waveguides, can dramatically affect the Bragg grating optical transmission spectra. We investigate the dependence of the grating spectrum on grating dimensions and etch depth, and show that our results have significant implications for designing narrow spectral width gratings in high index waveguides, either for minimizing HOM effects for conventional WDM filters, or potentially for designing devices to capitalize on very efficient HOM conversion.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. Topics in Applied Physics, vol 94: Silicon Photonics, Lorenzo Pavesi and David J. Lockwood, ed. (Springer-Verlag Heidelberg, 2004).
  2. R.A. Soref, J. Schmidtchen, and K. Petermann, �??Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SiO2,�?? IEEE J. Quantum Electron. 27, 1971-1974 (1991).
    [CrossRef]
  3. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, �??Design and fabrication of silicon photonic crystal optical waveguides,�?? J. Lightwave Technol. 18, 1402-1411 (2000).
    [CrossRef]
  4. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, �??Observation of stimulated Raman amplification in silicon waveguides,�?? Opt. Express 11, 1731-1739 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731</a>
    [CrossRef]
  5. R.E. Slusher and B.J. Eggleton, Nonlinear Photonic Crystals (Springer, 2003), pg 169.
  6. D.Wiesmann, C.Germann, D.Erni, and G.L.Bona, �??Apodized surface-corrugated gratings with varying duty cycles,�?? Photon. Technol. Lett. 12, 639-641 (2000).
    [CrossRef]
  7. T.E.Murphy, T.Hastings, and H.I.Smith, �??Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,�?? J. Lightwave Technol. 19, 1938-1942 (2001).
    [CrossRef]
  8. J.Canning, D.J.Moss, M.Faith, P.Leech, P.Kemeny, C.V.Poulsen, and O.Leistiko, �??Ultrastrong UV written gratings in PECVD grown germanosilicate rib waveguides,�?? Electron. Lett. 32, 1479-1480 (1996).
    [CrossRef]
  9. C.D. Poole, J.M. Wiesenfeld, D.J. DiGiovanni, A.M. Vengsarkar, �??Optical fiber-based dispersion compensation using higher order modes near cutoff,�?? J. Lightwave Technol. 12, 1746-1758 (1994).
    [CrossRef]
  10. T. Erdogan �??Fiber Grating Spectra,�?? J. Lightwave Technol. 15, 1277-1294 (1997)
    [CrossRef]
  11. B.J.Eggleton, P. S. Westbrook, C. A. White, C.Kerbage, R.S.Windeler, and G.L.Burdge, �??Cladding-moderesonances in air-silica microstructure optical fibers,�?? J. Lightwave Technol. 18, 1084-1100 (2000).
    [CrossRef]
  12. M.D. Feit and J.A. Fleck, �??Computation of mode properties in optical fiber waveguides by a propagating beam method,�?? Appl. Opt. 19, 1154-1164 (1980).
    [CrossRef] [PubMed]
  13. RSoft Design Group Inc., BeamPROP, 5.1.1 (RSoft Design Group Inc, 2003), pg. 17-19.
  14. J.J. Villa, �??Additional data on the refractive index of silicon,�?? Appl. Opt. 11, 2102-2103 (1972).
    [CrossRef] [PubMed]
  15. A. Othonos and K Kalli, Fiber Bragg Gratings (Artech House, 1999), pg. 95-105
  16. Po Shan Chan, H. K. Tsang, and C. Shu, �??Mode conversion and birefringence adjustment by focused-ionbeam etching for slanted rib waveguide walls,�?? Opt. Lett. 28, 2109-2111 (2003).
    [CrossRef] [PubMed]
  17. D.B. Stegall and T. Erdogan, �??Leaky Cladding Mode Propagation in Long-Period Fiber Grating Devices,�?? Photon. Technol. Lett. 11, 343-345 (1999).
    [CrossRef]

Appl. Opt.

Electron. Lett.

J.Canning, D.J.Moss, M.Faith, P.Leech, P.Kemeny, C.V.Poulsen, and O.Leistiko, �??Ultrastrong UV written gratings in PECVD grown germanosilicate rib waveguides,�?? Electron. Lett. 32, 1479-1480 (1996).
[CrossRef]

IEEE J. Quantum Electron.

R.A. Soref, J. Schmidtchen, and K. Petermann, �??Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SiO2,�?? IEEE J. Quantum Electron. 27, 1971-1974 (1991).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Lett.

Photon. Technol. Lett.

D.B. Stegall and T. Erdogan, �??Leaky Cladding Mode Propagation in Long-Period Fiber Grating Devices,�?? Photon. Technol. Lett. 11, 343-345 (1999).
[CrossRef]

D.Wiesmann, C.Germann, D.Erni, and G.L.Bona, �??Apodized surface-corrugated gratings with varying duty cycles,�?? Photon. Technol. Lett. 12, 639-641 (2000).
[CrossRef]

Other

Topics in Applied Physics, vol 94: Silicon Photonics, Lorenzo Pavesi and David J. Lockwood, ed. (Springer-Verlag Heidelberg, 2004).

RSoft Design Group Inc., BeamPROP, 5.1.1 (RSoft Design Group Inc, 2003), pg. 17-19.

A. Othonos and K Kalli, Fiber Bragg Gratings (Artech House, 1999), pg. 95-105

R.E. Slusher and B.J. Eggleton, Nonlinear Photonic Crystals (Springer, 2003), pg 169.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Cross-sectional profile of a rib waveguide: (a) a schematic, showing simulated mode profile for the fundamental mode and (b) a scanning electron micrograph of the waveguide used in this paper.

Fig. 2.
Fig. 2.

Experimental setup: (a) the FIB milled rib grating structure, (b) coupling to the grating waveguide, and (c) measuring the optical grating transmission spectrum.

Fig. 3.
Fig. 3.

Experimental (top) and theoretical (bottom) optical transmission spectrum of the surface grating from 1300 nm to 1680 nm using an unpolarized LED and optical spectrum analyzer with 0.4 nm resolution. The dotted lines are an aid to the eye, and the red arrow indicates the position of the fundamental Bragg resonance.

Fig. 4.
Fig. 4.

Grating transmission spectrum for the 1532 nm and 1554 nm resonances measured with a high power ASE-EDFA source for both TE and TM polarizations at a resolution of 80 pm.

Fig. 5.
Fig. 5.

Effective index versus wavevector of the first 24 TE modes of the rib waveguide are represented by the colored lines. Intersection with the thick black line (λ/2) indicates a diagonal solution of the Bragg equation.

Fig. 6.
Fig. 6.

Mode profiles for the first 21 modes of the rib waveguide. As the mode profiles are horizontally symmetric, only the right half of each profile is displayed

Fig. 7.
Fig. 7.

(a) Top: Bragg grating coupling coefficient of the first 21 modes of the rib waveguide (b) Middle: leakage rates of the HOM as measured from BPM simulations and (c) Bottom: figure of merit representing how well the mode lobes fit in the both rib and slab regions (0.0 = poor, 1.0 = good spatial overlap).

Fig. 8.
Fig. 8.

Schematic representation of the spatial overlap of the mode with the slab region. For modes that do not fit an integer number of lobes (a) in the slab, the figure of merit is defined as “0”, while for modes that fit an integer number of lobes in the slab (b) and hence have good overlap with the slab, the figure of merit is defined to be “1”.

Fig. 9.
Fig. 9.

Theoretical coupling coefficients (κ) for grating depths of 40nm, 200nm and 400 nm. The overall envelop increases in strength and shifts to longer wavelength (and lower order modes) as the grating probes more of the fundamental mode. The arrow at the top right indicates the position of the fundamental grating resonance.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

W H α + h / H 1 ( h / H ) 2 ,
h H 1 2 ,
λ = ʌ ( n inc + n scat ) ,
T i = 1 tanh 2 ( κ i L ) ,
κ i = ( π λ ) Δ n ( x , y ) E 0 ( x , y ) E i * ( x , y ) dxdy .
E ( x , y , 0 ) = Δ n ( x , y ) E 0 ( x , y ) .
P ( z ) = E ( x , y , 0 ) E * ( x , y , z ) dxdy ,
α i = ( λ π ) κ i .

Metrics